Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces

@article{Santin2021SamplingBA,
  title={Sampling based approximation of linear functionals in reproducing kernel Hilbert spaces},
  author={Gabriele Santin and Toni Karvonen and Bernard Haasdonk},
  journal={BIT Numerical Mathematics},
  year={2021},
  volume={62},
  pages={279-310}
}
In this paper we analyze a greedy procedure to approximate a linear functional defined in a reproducing kernel Hilbert space by nodal values. This procedure computes a quadrature rule which can be applied to general functionals. For a large class of functionals, that includes integration functionals and other interesting cases, but does not include differentiation, we prove convergence results for the approximation by means of quasi-uniform and greedy points which generalize in various ways… 

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